Dichotomous Consistency And Adaptive Event Trigger Consistency Of Multi-agent Systems

In recent years,with the development of artificial intelligence,collaborative control of multi-agent systems has become a hot issue,where the research on consensus has solved many complex problems in theory and in real life.This paper investigates the bipartite consensus problem of multi-agent systems and the consensus problem based on adaptive event-triggering.The main contents include:1.The background of consensus for multi-agent systems is introduced.The research status about the consensus problem of time-delay systems and the consensus problem based on adaptive event-triggering are described.2.The knowledge of graph theory and matrix theory used in this paper is introduced,and some basic lemmas are introduced.3.Consensus protocol is designed for the bipartite consensus problem of multi-agent systems with time-varying delays.Lyapunov-Krasovskii functional is constructed and the linear matrix inequality theory and the method of free matrix are used to obtain the sufficient conditions for bipartite consensus of multi-agent systems.The cases of fixed topology and switching topologies are both investigated and the method of average dwell time is used to get sufficient conditions to guarantee bipartite consensus when the systems have switching topologies.4.The bipartite consensus problem is investigated for multi-agent systems with time-varying delays based on time-delay partitioning method and the corresponding consensus protocols are designed for first-order and second-order systems,respectively.Lyapunov-Krasovskii functional is constructed based on the method of delay partitioning.The linear matrix inequality theory and free matrix integral inequality are used to obtain sufficient conditions for bipartite consensus of first-order and second-order multi-agent systems,respectively.5.For the event-triggered consensus problem of multi-agent systems,the edge-based and node-based distributed adaptive consensus protocols are designed,respectively.Sufficient conditions for the achievement of consensus of corresponding systems are given.Moreover,Zeno behavior for the corresponding closed-loop system is excluded.